       NDSolve memory management problem

• To: mathgroup at smc.vnet.net
• Subject: [mg101868] NDSolve memory management problem
• From: David Szekely <dr.szekely at gmail.com>
• Date: Mon, 20 Jul 2009 06:01:17 -0400 (EDT)

```Hi there!
I'm currently trying to run a simulation in Mathematica using NDSolve in several dimensions. However, it tends to chew up system memory very quickly and give the standard:
"No more memory available.
Mathematica kernel has shut down.
Try quitting other applications and then retry."
message.
Here's some code for the heat equation in 4 dimensions over relatively small ranges to show what I mean:
i = 0;
sol = NDSolve[{D[u[t, x, y, z], t] ==
D[u[t, x, y, z], x, x] + D[u[t, x, y, z], y, y] +
D[u[t, x, y, z], z, z],
u[0, x, y, z] == 0,
u[t, 0, y, z] == Sin[t],
u[t, 40, y, z] == 0,
u[t, x, 0, z] == Sin[t],
u[t, x, 40, z] == 0,
u[t, x, y, 0] == Sin[t],
u[t, x, y, 40] == 0},
{u}, {t, 0, 100}, {x, 0, 40}, {y, 0, 40}, {z, 0, 40},
MaxSteps -> Infinity, MaxStepSize -> 1,

EvaluationMonitor :> If[t > i,
Print[{t, MemoryInUse[]/1024^2 // N}];
i += 10;]

]
MemoryInUse[]/1024^2 // N

The only solutions I need are at t = 0, 5, 10, 15 etc.. Ideally, what i'd like to be able to do is add a function in "EvaluationMonitor" which removes all values of t other than the ones that I need *as it solves the system*. This would significantly reduce the strain on system memory. I would greatly appreciate help on this problem! Adding more memory is not a good solution since my actual problem kills a system with 12 Gb of memory :(

```

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